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1、MethodsofMultivariateAnalysisSecondEditionALVINC.RENCHERBrighamYoungUniversityAJOHNWILEY&SONS,INC.PUBLICATIONThisbookisprintedonacid-freepaper.∞Copyrightc2002byJohnWiley&Sons,Inc.Allrightsreserved.PublishedsimultaneouslyinCanada.Nopartofthispublicationmaybereproduced,
2、storedinaretrievalsystemortransmittedinanyformorbyanymeans,electronic,mechanical,photocopying,recording,scanningorotherwise,exceptaspermittedunderSections107or108ofthe1976UnitedStatesCopyrightAct,withouteitherthepriorwrittenpermissionofthePublisher,orauthorizationthrou
3、ghpaymentoftheappropriateper-copyfeetotheCopyrightClearanceCenter,222RosewoodDrive,Danvers,MA01923,(978)750-8400,fax(978)750-4744.RequeststothePublisherforpermissionshouldbeaddressedtothePermissionsDepartment,JohnWiley&Sons,Inc.,605ThirdAvenue,NewYork,NY10158-0012,(212
4、)850-6011,fax(212)850-6008.E-Mail:PERMREQ@WILEY.COM.Fororderingandcustomerservice,call1-800-CALL-WILEY.LibraryofCongressCataloging-in-PublicationDataRencher,AlvinC.,1934–Methodsofmultivariateanalysis/AlvinC.Rencher.—2nded.p.cm.—(Wileyseriesinprobabilityandmathematicals
5、tatistics)“AWiley-Intersciencepublication.”Includesbibliographicalreferencesandindex.ISBN0-471-41889-7(cloth)1.Multivariateanalysis.I.Title.II.Series.QA278.R452001519.535—dc212001046735PrintedintheUnitedStatesofAmerica10987654321Contents1.Introduction11.1WhyMultivaria
6、teAnalysis?,11.2Prerequisites,31.3Objectives,31.4BasicTypesofDataandAnalysis,32.MatrixAlgebra52.1Introduction,52.2NotationandBasicDe?nitions,52.2.1Matrices,Vectors,andScalars,52.2.2EqualityofVectorsandMatrices,72.2.3TransposeandSymmetricMatrices,72.2.4SpecialMatrices,8
7、2.3Operations,92.3.1SummationandProductNotation,92.3.2AdditionofMatricesandVectors,102.3.3MultiplicationofMatricesandVectors,112.4PartitionedMatrices,202.5Rank,222.6Inverse,232.7PositiveDe?niteMatrices,252.8Determinants,262.9Trace,302.10OrthogonalVectorsandMatrices,312
8、.11EigenvaluesandEigenvectors,322.11.1De?nition,322.11.2I+AandI?A,332.11.3tr(A)and
9、A
10、,342.11.4PositiveDe?niteandSemid
